What do I do if the first (power) light is lit on my Gateway Hub, but the second (Ethernet) light isn't?

This indicates that the Ethernet port is not connected to your router.

Make sure there is an Ethernet cable between the “LAN” port on the Power Supply and one of the “output” ports on your router

Check the Ethernet cable between the Power Supply and the Hub and the Power Supply and the router. There are four pairs of wires – eight wires – in an Ethernet cable, four providing power and four providing communications. In some cases, the wires providing power may be intact and one or more of the wires providing communications may be severed, so the Hub may be getting power but not able to communicate with the router. Try connecting the Hub to the Power Supply with a different Ethernet cable.